View
217
Download
0
Category
Preview:
Citation preview
Int. J. Electrochem. Sci., 9 (2014) 955 - 974
International Journal of
ELECTROCHEMICAL SCIENCE
www.electrochemsci.org
Structural, Electronic and Optical Properties in Earth-
Abundant Photovoltaic Absorber of Cu2ZnSnS4 and
Cu2ZnSnSe4 from DFT calculations
A. H. Reshak1,2,*
, K. Nouneh3, I.V. Kityk
4,7, Jiri Bila
5, S. Auluck
6, H. Kamarudin
2, Z. Sekkat
3,8
1 New Technologies - Research Center, University of West Bohemia, Univerzitni 8, Pilsen 306 14,
Czech Republic
2 Center of Excellence Geopolymer and Green Technology, School of Material Engineering,
University Malaysia Perlis, 01007 Kangar, Perlis, Malaysia 3Moroccan Foundation for Advanced Science, Innovation and Research (MAScIR), Optics &
Photonics, ENSET, Av. Armée Royale 10100, Rabat, Morocco 4Electrical Engineering Department, Czestochowa University of Technology, Armii Krajowej 17,
Czestochowa, Poland 5Department of Instrumentation and Control Engineering, Faculty of Mechanical Engineering, CTU in
Prague, Technicka 4, 166 07 Prague 6, Czech Republic 6Council of Scientific and Industrial Research - National Physical Laboratory Dr. K S Krishnan Marg,
New Delhi 110012, India 7Eastern European University, Physical Department, Al Voli 6, Lutsk, Ukraine
8University Mohamed V-Agdal, Faculty of Sciences, Rabat, Morocco
*E-mail: maalidph@yahoo.co.uk
Received: 24 August 2013 / Accepted: 7 October 2013 / Published: 1 December 2013
DFT analyses of band structure dispersion and of contribution of different anionic sub-groups to the
studied electronic structure together with the anisotropy of optical functions were performed for the
two promising solar cell crystals Cu2ZnSnS4 and Cu2ZnSnSe4. We have applied the state-of-the-art
full potential linear augmented plane wave (FPLAPW) method in a scalar relativistic version.
Exchange and correlation potential were introduced within a framework of the local density
approximation (LDA) and gradient approximation (GGA). We show that Cu2ZnSnS4 as well as
Cu2ZnSnSe4 crystals possess a direct energy band gap situated around the center of the BZ. Careful
analysis of the total density of states together with the partial contribution of the particular orbital were
performed for evaluations of contribution of corresponding bonds to the origin of the chemical bonds.
Role of replacing of S by Se is analyzed in the details for the electronic density of states with respect to
the nature of chemical bonds. The principal analysis is performed for the dispersion of the optical
constants. The influence of the different chemical bonds into the dispersion of the optical functions is
analyzed in order to optimize the optical features with respect to the requirements of the solar cell
elements.
Int. J. Electrochem. Sci., Vol. 9, 2014
956
Keywords: CZTS Kesterites;Cu2ZnSnS4; optical functions; DFT band structure calculations
1. INTRODUCTION
To decrease the consumption of fossil fuels, energy sources like solar energy must be
advanced. Solar cells are an alluring energy source, as they do not cause any detrimental emissions. In
the many solar cell materials as a rule the Si-based solar cell is mostly used. Ideally, the absorber
material of an efficient terrestrial solar cell should be a direct bandgap semiconductor with a bandgap
of 1.5 eV with a high solar optical absorption (~105/cm) high quantum efficiency of excited carriers,
long diffusion length, low recombination velocity, and should be able to form a good electronic
junction (homo/hetero/Schottky) with suitably compatible materials. With high optical absorption, the
optimum thickness of an absorber in a solar cell is of the order of the inverse of the optical absorption
coefficient and thus it must be a thin-film. The I–III–VI2 ternary compounds like CIS and CIGS etc,
and their alloys CuInxGa1−xSe2 (CIGSe) are considered to be suitable absorber materials in low-cost
and high-efficiency thin-film solar-cell technologies. Recently, the Cu2ZnSnS4 (CZTS) absorber has
drawn an increasing amount of attention within thin-film solar cell technology owing to its optimal
single-junction band gap (~1.5 eV) and high absorption coefficient (~105 cm−1) [1–3], in which the
expensive group-III elements (i.e., In and Ga) are substituted by group-II-IV elements (e.g. Zn plus
Sn), thereby forming the I2–II–IV–VI4 quaternary compound Cu2ZnSnSe4 (CZTSe) and its sulfide
counterpart Cu2ZnSnS4 (CZTS). The band-gap energy Eg of the CIGSe alloy can be tuned from 1.04
to 1.68 eV and the gap energies of CZTS and CZTSe are around 1.0–1.5 eV, which is suitable for
photovoltaic applications. Moreover, knowledge of the optical properties, such as the dielectric
function and the optical absorption coefficient, is required to analyze optical measurements as well as
to optimize the solar cell devices.
Recently, a solar-cell conversion efficiency of 10.1% was reported [4] for the mixed sulfide–
selenide CZTSSe absorber made by hydrazine-based solution processing. For the nominal intrinsic
CZTS, the highest efficiency has reached 8.4% [5]. To obtain this high efficiency, the Cu-poor and Zn-
rich condition in CZTS is currently necessary.
The CZTS thin film exists in two types of crystal structures kesterite and stannite [6]. Schorr
[7,8] has established that both crystal structures are tetragonal, except the difference between them is
the site position of their Cu and Zn atoms. The crystal structure of isomorphic crystals is important
infor calculation of their band structure. [9]. Their electronic properties and crystal structures are
analogous to those of the parent CIGS, while their constituent elements are naturally copious and
nontoxic. According to the Shockley–Queisser limit the Cu2ZnSnSxSe1−x have gaps and usually are
used as absorbers in thin film solar cells favoring growing energy conversion efficiency [10,11].
Though, the understanding of the properties of Cu2ZnSnS4 and Cu2ZnSnSe4 for the different phases is
still rather cursory, recent studies have reported their structural,[12-14] electronic [12,13,15] and
defect properties.[16,17]. Nozaki et al. [18] experimentally determined the crystal structure of
Cu2ZnSnS4 thin films fabricated by vapor-phase sulfurization using X-ray anomalous dispersion. He
and Shen [19] perform first principles study of elastic and thermo-physical properties of kesterite type
Int. J. Electrochem. Sci., Vol. 9, 2014
957
Cu2ZnSnS4 , using VASP code. They found that the calculated lattice constants are in good agreement
with the experimental data. Persson [20] studied the electronic and the optical properties of Cu2ZnSnS4
and Cu2ZnSnSe4 using FPLAPW-LDA. Chen et al. [21] have used the VASP code to study the
structural and electronic properties of Cu2ZnSnS4 and Cu2ZnSnSe4.
From above it is clear that there is no comprehensive research work neither experimental nor
theoretical one were done for these compounds Cu2ZnSnS4 and Cu2ZnSnSe4. Thus we thought it
would be worthwhile to perform such comprehensive investigation for such kind of important
materials. Therefore we have calculated the electronic band structure, density of states, electronic
charge density and the optical properties of Cu2ZnSnS4 and Cu2ZnSnSe4 using the full potential
method.
The main goal of the present work is to perform DFT analysis of the band structure dispersion
of Cu2ZnSnS4 and Cu2ZnSnSe4 and also to perform analysis of contribution of different anionic sub-
groups to the studied electronic structure. Following these calculations the analysis of the electronic
density of states and the modeling of the corresponding optical constants dispersions will be
calculated. Section 2 presents principal crystallochemistry analysis and applied calculation technique.
Section 3 is devoted to presentation of the band structure calculations, electronic density of states, and
the dispersion of principal optical functions.
2. CRYSTAL STRUCTURES AND COMPUTATIONAL DETAILS
Table 1. Crystallographic lattice parameters for the compounds Cu2ZnSnS4 [15] and Cu2ZnSnSe4 [16]
Cu2ZnSnS4 Cu2ZnSnSe4
SG I 4 2m (no. 121)
a (Å) 5.434(1) 5.6882(2)
c (Å) 10.856(1) 11.3378(9)
4d (0 ½ ¼) 0.5Cu+0.5Zn Cu
2a (0 0 0 ) Cu Zn
2b (0 0 ½) Sn Sn
8i (x x z) S (x=0.75617(8),
z= 0.87208(5)
Se (x=0.2587(2),
z=0.3714(2))
Crystallographic parameters for the chalcogenide Cu2ZnSnS4 [22] and Cu2ZnSnSe4 [23] are
given in Table 1. The second coordination number of chalcogen atoms in the compound Cu2ZnSnS4
and Cu2ZnSnSe4 were presented in Fig. 1. Generally consideration of the second anionic group is
very efficient way to analyze the chalcogenide structures [24]. One can see cubooctahedra containing
chalcogen atoms and cationic atoms are situated opposite triangle faces which corresponds to their
tetrahedral coordination. Second coordination is formed by chalcogen atoms and define principal inter-
atomic distances within the anionic group of Cu2ZnSnS(Se)4 system. Inter-atomic distances chalcogen-
chalcogen are slightly greater with respect to the sum of their atomic radiuses and the bond lengths
Int. J. Electrochem. Sci., Vol. 9, 2014
958
anion-cation are shortened (rSe-2
= 1.91, rS-2
= 1.82, rCu+1
= 0.96, rZn+2
= 0.83, rSn+4
= 0.71 [25]). This
one confirms prevailingly ionic cationic-anionic origin of the chemical bonds.
Figure 1. Second coordination surrounding of chalcogen atoms and inter-atomic distances within the
anionic group of Cu2ZnSnS(Se)4 system. Inter-atomic distances chalcogen-chalcogen are
slightly higher with respect the sum of their atomic radiuses and the bond lengths anion-cation
are shortened (rSe-2
= 1.91, rS-2
= 1.82, rCu+1
= 0.96, rZn+2
= 0.83, rSn+4
= 0.71 [17]). This one
confirm prevailingly ionic cationic-anionic origin of the chemical bonds
We have applied the state-of-the-art full potential linear augmented plane wave (FPLAPW)
method in a scalar relativistic version as embodied in the WIEN2k code [26]. This is an
implementation of the DFT with different possible approximations for the exchange-correlation (XC)
potential. Exchange and correlation potential were introduced within a framework of the local density
approximation (LDA) [27] and gradient approximation (GGA) [28], which is build applying exchange-
correlation energy optimization to evaluate the minimum of total energy. We also have used Engel-
Int. J. Electrochem. Sci., Vol. 9, 2014
959
Vosko generalized gradient approximation (EV-GGA) [29] and the modified Becke-Johnson potential
(mBJ) [30], which serve for optimization of the corresponding potential for electronic band structure
calculations. These methods are very efficient for studies of the semiconducting materials with
relatively narrow band energy gaps. The FP-LAPW method is more efficient for the materials
possessing different degree of wave functions localization. That means for the crystals where exists a
coexistence of delocalized covalence and high localized d-p chemical bonds use of the mentioned
methods may be very powerful [31,32]. The Kohn-Sham equations were solved using a basis of linear
APW’s. The potential and charge density distributions intra the muffin-tin (MT) spheres are expanded
in spherical harmonics with orbital number lmax=8 and nonspherical components up to lmax=6. In the
interstitial space the potential and the charge density were represented by Fourier series. The chosen
MT sphere radii of Cu2ZnSnS4 were 2.29, 2.35, 2.31, 2.03 a.u. for Cu, Zn, Sn, and S, respectively and
for Cu2ZnSnSe4 are 2.38, 2.46, 2.44 and 2.11 a.u., for Cu, Zn, Sn and Se, respectively. The structure of
the chalcogenide Cu2ZnSnS4 and Cu2ZnSnSe4 was optimized by minimization of forces acting on the
atoms to get optimized with respect to the mixed relaxed geometry. Self-consistency was achieved just
at 300 k
points in the irreducible Brillouin zone (IBZ). However for the optical functions it was
necessary to use more number of the points within the BZ (about 500 k
points in the IBZ).
3. RESULTS AND DISCUSSION
3.1 Band structure parameters and density of state
Figure 2. Calculated band structure using mBJ.
The study of band structure for the photovoltaic material and particularly for the crystal
presents very important task. It allow to evaluate the spectral distribution of the absorption, charge
Int. J. Electrochem. Sci., Vol. 9, 2014
960
density distribution, their mobility etc. The evaluated optical features may serve as a basis for the
further optimization of the electronic properties in the desired direction.
The calculated band structure dispersion in k-space along high symmetry directions in the BZ,
the total and partial density of states are presented in Fig. 2 and 3. Following Fig.2, one can see that
both Cu2ZnSnS4 as well as Cu2ZnSnSe4 crystals possess a direct energy band gap situated around the
center of the BZ.
(a) (b)
(c) (d)
(e) (f)
Int. J. Electrochem. Sci., Vol. 9, 2014
961
(g) (h)
(i) (j)
(k) (l)
Figure 3. Calculated total and partial densities of states (States/eV unit cell) using LDA, GGA,
EVGGA and mBJ.
The calculated values of the band gaps are 0.54 eV and 0.22 eV for Cu2ZnSnS4 and
Cu2ZnSnSe4, respectively. It is principal that the energy gap is reduced with replacing S to Se, this
Int. J. Electrochem. Sci., Vol. 9, 2014
962
reduction is attributed to the fact that Se atoms have bigger radius (1.17 Å) than S (1.17 Å) and the
atomic terms of pSe lie higher in energy the atomic terms of pS.
These terms are responsible for the formation of the VB . In the periodic table when we move
down in group there is an increase in the bond length of the compounds (see Fig. 1) resulting in
decrease of the band gap. In other hand, the electronegativity value of S is 2.58 and 2.55 for Se,
respectively. Thus, when S is replaced by Se it leads to an increase of the bond length. Oppositely
increase in the bond length results in a decrease in the band gap. Following Fig. 2, it is clear that the
conduction band of Cu2ZnSnSe4 is shifted towards Fermi level with respect to Cu2ZnSnS4.
The total density of states (TDOS) for Cu2ZnSnSe4 and Cu2ZnSnS4 were calculated using four
type of XC screening potentials. Our calculations confirm the substantial influence of different kinds
of XC potentials on the electronic structure features. We should remind that for the all full potential
methods the potential and charge densities are expanded into lattice harmonics inside each atomic
sphere and as a Fourier series in the interstitial region. As a remarkable finding, mBJ [42-46] form
gives energy band gap larger then LDA, GGA, and EVGGA approaches. Thus we will demonstrate
only the results obtained by mBJ.
For these crystals the unit cell contains four atoms. In order to understand the contribution of
each orbital in these atoms we investigate the angular momentum decomposition of the atoms
projected density of states (PDOS) as illustrated in the Fig. 3 c-l. The PDOS helps to identify the
angular momentum character of the various structures; the lowest structure extended from -15.0 eV up
to -5.0 eV originated mainly from Sn-s, Se/S-s, Se/S-p, Sn-p, Zn-d states with small admixture of Zn-
s/p, Se-d, Cu-s/p and Sn-d states. All these orbitals are spatially delocalized. Next energy fragment -
from -5.0 eV till Fermi level (EF) originates from more localized Cu-d, and delocalized Se/s-p, Sn-p
states with small contribution from Sn-s/d, Zn-s/p, Se-d, Cu-s/p states. Finally the structure from the
conduction band minimum and above presents an admixture of Cu-s/p, Sn-p/d, Zn-s/p, Se-s/p/d and S-
p states. One can see a strong hybridization between Cu-p, Zn-d and Sn-d states and also some overlap
between Se-s and Sn-s states, at around -13.5 eV. At -8.0 eV there is relatively strong hybridization
between Se-p and Sn-s, Sn-s and S-p states as well as between Zn-s/p and Cu-s/p states. At the
energies lying between -3.5 eV to -1.0 eV there is a strong hybridization between Se-d and Se-p.
Between 1.0 eV to 4.0 eV there occurs also a strong hybridization between Sn-s and Se/S-p states and
also between Sn-d and Cu-s states.
3.2. Electron charge density
Now we will analyze and express the electronic charge density of Cu2ZnSnSe4 and Cu2ZnSnS4,
to obtain a deeper insight into the electronic structure, we displayed the electronic charge density
contour in the (203) crystallographic plane as shown in Fig. 4a. The contour plot shows partial ionic
and strong covalent bonding between Cu-S/Se and Zn-S/Se atoms depending on Pauling electro-
negativity difference of Cu (1.90), Zn (165) Sn (1.96), and S/Se (2.58/2.55) atoms. From these contour
plots one can see that the majority of Cu, Zn, and Sn electronic charge is transferred to S/Se atom. This
can be seen easily by the color charge density scale where blue color (+1.0000) corresponds to the
Int. J. Electrochem. Sci., Vol. 9, 2014
963
maximum charge accumulating site. The charge density along Cu-S/Se, Zn-S/Se bonds is pronounced.
It is clear that when we replace S by Se the charge density decreases. As it is clear from Fig. 4a, that
the charge density around the S is greater than the Se. the bond length between Zn and Se decrease as
we replace S by Se which is not shown in Fig.4a. In additional we have plotted the electronic charge
density contour in the (100) crystallographic plane as shown in Fig.4b. In this plane only three atoms
namely Zn, Cu and Sn, from both of Cu2ZnSnSe4 and Cu2ZnSnS4 are contributed.
(a)
(b)
Figure 4. Electronic Charge density
Int. J. Electrochem. Sci., Vol. 9, 2014
964
3.3. Dispersion of optical permittivity
The dispersion of optical permittivity was evaluated from the energy eigenvalues and electron
wave functions . Since the crystals are crystallized in tetragonal structure, following this symmetry
one can observe only two non-zero components of second order dielectric tensor, i.e. )( xx and
)( zz . The two tensor components of the imaginary part of dielectric function (permittivity)
completely define the principal linear optical dispersions responsible for absorption , refractive indices
and reflection spectra. It should be emphasized that the contribution of the different BZ points will be
different due to the van Howe singularities [33]. The dispersion of imaginary part can be calculated
using the expression give in Ref. 34:
knnknkknj
nn
i
ij EEffknpnknkpknVm
e1
422
22
2
In this expression the indices m and e mean mass and charge of electron and ω represent the
varying optical frequency, V stand for volume of the unit cell, in bracket notation p represent the
momentum operator, kn describes the crystal wave function with crystal momentum k and σ spin
which correspond to the eigenvalue knE . The Fermi occupation distribution function corresponds to
knf which makes sure the counting of transition from occupied to unoccupied state and the term
knnk EE shows the condition for conservation of total energy. The phonons have negligible
contribution to )(2 , however their mainly define the broadening of the spectral lines [35], which
may be fitted following the experimental data. Therefore we ignore the phonons contribution involved
in the indirect inter-band transition introducing some experimentally obtained spectral half-width and
only considering principal direct band transition between occupied VB and unoccupied CB states with
the corresponding dipole matrix transitions moments. The spectral peaks in the optical response are
caused by the allowed electric-dipole transitions between the VB and CB and here main contributions
give the mentioned van Howe singularities. To identify these structures we analyze magnitudes of
corresponding optical matrix elements.
It is well know that the DFT calculations usually underestimate the energy gaps with respect to
the experimentally obtained gaps. Thus we have applied the scissors correction to the optical properties
in order to fit the value of the calculated energy gap exactly to the measured one. This procedure was
successively used by several workers for different organic and inorganic compounds [36]. The scissors
correction is the difference between the calculated and measured energy gaps. After applying the
scissors correction there occurs a significant effect on the magnitude, peaks positions and the structure
of principal optical functions for the materials studied. This could arise from differences in the band
structures and wave-functions.
The dispersion spectra of )(2 as illustrated in Figs. 5a and b, possess the threshold energy
(first critical point) of the dielectric function occurring at 1.6 eV for Cu2ZnSnS4 and 1.44 eV for
Cu2ZnSnSe4 crystals. The main structure of )(2 xx
and )(2 zz
is extended between the thresholds and
14.0 eV. One can see that the spectral structure for )(2 xx
and )(2 zz
for the both crystals are similar
except some minor spectral deviations. Moreover, the whole structure is shifted towards lower energies
Int. J. Electrochem. Sci., Vol. 9, 2014
965
when we replace S by Se due to the band gap decreases and the changes in the band energy
dispersions.
(a)
(b)
Int. J. Electrochem. Sci., Vol. 9, 2014
966
(c)
(d)
Int. J. Electrochem. Sci., Vol. 9, 2014
967
(e)
(f)
Int. J. Electrochem. Sci., Vol. 9, 2014
968
(g)
(h)
Int. J. Electrochem. Sci., Vol. 9, 2014
969
(i)
(j)
Int. J. Electrochem. Sci., Vol. 9, 2014
970
(k)
(l)
Figure 5. Calculated xx
2 (dark solid curve-black color online) and zz
2 (light dashed curve-red
color online) dispersion spectra for different apporaches: mBJ with scissors correction for (a)
Cu2ZnSnS4 and (b) Cu2ZnSnSe4; Calculated xx
1 (dark solid curve-black color online)
Int. J. Electrochem. Sci., Vol. 9, 2014
971
and zz
1 (light dashed curve-red color online) dispersion spectra: mBJ with scissors
correction for (c) Cu2ZnSnS4 and (d) Cu2ZnSnSe4; Calculated xxn (dark solid curve-black
color online) and zzn (light dashed curve-red color online) dispersion spectra: mBJ with
scissors correction for (e) Cu2ZnSnS4 and (f) Cu2ZnSnSe4; Calculated xxI (dark solid
curve-black color online) and zzI (light dashed curve-red color online) dispersion spectra:
mBJ with scissors correction for (g) Cu2ZnSnS4 and (h) Cu2ZnSnSe4; Calculated xxR (dark
solid curve-black color online) and zzR (light dashed curve-red color online) dispersion
spectra: mBJ with scissors correction for (i) Cu2ZnSnS4 and (j) Cu2ZnSnSe4; Calculated xxL
(dark solid curve-black color online) and zzL (light dashed curve-red color online)
dispersion spectra: mBJ with scissors correction for (k) Cu2ZnSnS4 and (m) Cu2ZnSnSe4.
Fig. 5a and b, confirm that there exist a considerable anisotropy between )(2 xx
and )(2 zz
spectra. Possessing the dispersion of imaginary part of dielectric function the real part can be evaluated
using Kramers-Kronig integral relations [37]. The calculated dispersions of real part of dielectric
function )(1 xx
and )(1 zz
are shown in Fig. 5c and d. Again it show considerable anisotropy among
)(1 xx
and )(1 zz
except at the low energy tail. The calculated optical dielectric constants at zero
energy limit )0(1
xx and )0(1
zz are equal to 5.94, 6.61 and 7.04, 7.80, for Cu2ZnSnS4 and Cu2ZnSnSe4
,respectively.
Fig.5 (e-l) shows the dispersion for non zero tensor components of refractive index )(n ,
extinction coefficient )(k , absorption coefficient )(I , reflectivity spectra )(R and energy loss
function )(L . Complex refractive index ( )()()(~ iknn ) describes the refraction as well as well
absorption of the compounds. It consists of two parts; the real part , )(n , is just the refractive index
second-order tensor while the other part, )(k , is the extinction tensor which describes the loss of
photon energy during propagation through the optical medium. As these compounds have tetragonal
symmetry, only two tensor components (parallel and perpendicular to the c- axis with respect to the
polarization of the optical field) are required to describe all the optical properties. The parallel and
perpendicular components of refractive index ( IIn and n , respectively) and extinction coefficient
( IIk and k ) define all the linear optical properties. The calculated non zero tensor components of static
refractive index )0(xx
n and )0(zz
n are 2.42 and 2.56 for Cu2ZnSnS4 and 2.65, 2.79 for Cu2ZnSnSe4.
Penn’s model [38] claims that )0(1 depends on band gap of the material and )0(1 is directly related
to the )0(n by the relation )0()( 1 n . They are enhanced beyond the zero frequency limits
reaching their maximum values. Beyond the maximum value they start to decrease and with few
oscillations they go beyond unity. In this region (n<1) the phase velocity of the photons increases
approaching to universal constant (C). However the group velocity always remains less than the C, as a
consequence the relativity relations are not effected [39]. The spectra are shifted towards lower energy
by changing the cations from S to Se. The variation is in accordance to the decreasing in the band gap.
The calculated refractivity for Cu2ZnSnS4 and Cu2ZnSnSe4, are illustrated in Figs. 5 e and f.
Int. J. Electrochem. Sci., Vol. 9, 2014
972
The absorption spectra of Cu2ZnSnS4 and Cu2ZnSnSe4 (Figs. 5 g and h) show that these
materials start absorbing the radiation at the wavelength below 775 nm and 861.1 nm, respectively.
The absorption spectra show the highest value at 13.5 eV corresponding to the minimum value of
)(1 and )(2 shown in Fig.5a-d.
Frequency dependent reflectivity )(zzR and )(xxR parallel and perpendicular spectra
components to the electric field, are calculated and depicted in Figs. 5 i and j. The reflectivity spectra
of the compounds start from the zero frequency which defines the static part of the reflectivity
components )0(zzR and )0(xxR . These values are equal to 0.17 and 0.18 for Cu2ZnSnS4 and 0.20, 0.22
for Cu2ZnSnSe4 single crystals. The reflectivity spectra of the compounds are spectrally red shifted
during replacing anions of S by Se. The )(L described the energy loss of fast electron traveling in
the material (Figs. 5 k and l). The sharp spectral peaks produced in )(L around 12.5 eV are due to
the occurence of plasmon excitations [40].
4. CONCLUSION
The full potential linear augmented plane wave (FPLAPW) method in a scalar relativistic
version, was applied for calculating the electronic structure of the two promising solar cell crystals
Cu2ZnSnS4 and Cu2ZnSnSe4. The PDOS helps to identify the angular momentum character of the
various structures, and to study the degree of the hybridization between states. We found that there
exists weak/strong hybridization between the states. The optical spectra are shifted towards lower
energy by changing the cations from S to Se. The variation is in accordance to the decreasing in the
band gap. The absorption spectra of Cu2ZnSnS4 and Cu2ZnSnSe4 show that these materials start
absorbing the radiation at the wavelength below 775 nm and 861.1 nm, respectively. The absorption
spectra show the highest value at 13.5 eV corresponding to the minimum value of )(1 and )(2 . It
was found that the calculated optical dielectric constants at zero energy limit )0(1
xx and )0(1
zz are
equal to 5.94, 6.61 and 7.04, 7.80, for Cu2ZnSnS4 and Cu2ZnSnSe4 ,respectively.
AKNOWLEDEGMENT
The result was developed within the CENTEM project, reg. no. CZ.1.05/2.1.00/03.0088, co-funded by
the ERDF as part of the Ministry of Education, Youth and Sports OP RDI programme. School of
Material Engineering, Malaysia University of Perlis, Malaysia.
References
1. S. Siebentritt, S. Schorr, Prog. Photovoltaics Res. Appl. 20 (2012) 512.
2. D.B. Mitzi, O. Gunawan, T.K. Todorov, K. Wang, S. Guha, Sol. Energy Mater. Sol. Cells 95
(2011) 1421.
3. S. Ahmed, K.B. Reuter, O.Gunawan, L. Guo, L.T. Romankiw,H. Deligianni, Adv. Energy Mater. 2
(2012) 253
4. D. Aaron, R. Barkhouse, O. Gunawan, T. Gokmen, T.K. Todorov, D.B. Mitzi, Prog. Photovoltaics
Res. Appl. 20 (2012) 6.
Int. J. Electrochem. Sci., Vol. 9, 2014
973
5. B. Shin, O. Gunawan, Y. Zhu, N.A. Bojarczuk, S.J. Chey, S. Guha, Prog. Photovoltaics Res. Appl.
Vol 21, (2013) pp. 72-76
6. S.R. Hall, J.T. Syzmanski, J.M. Stewart, Can. Miner. 16 (1978) 131.
7. S. Schorr, Thin Solid Films 515 (2007) 5985.
8. S. Schorr, H.J. Hoebler, M. Tovar, Eur. J. Mineral. 19 (2007) 65.
9. J. Paier, R. Asahi, A. Nagoya, G. Kresse, Phys. Rev. B 79 (2009) 115126.
10. K. Todorov, K. B. Reuter, and D. B. Mitzi, Adv. Mater. Weinheim, Ger. 22, (2010) E156
11. A. Redinger, D. M. Berg, P. J. Dale, and S. Siebentritt, J. Am. Chem. Soc. 133, (2011) 3320
12. C. Persson, J. Appl. Phys. 107, (2010) 053710
13. S. Chen, X. G. Gong, A. Walsh, and S.-H. Wei, Appl. Phys. Lett. 94, (2009) 041903
14. S. Chen, A. Walsh, Y. Luo, J.-H. Yang, X. G. Gong, and S.-H. Wei, Phys. Rev. B 82, (2010)
195203
15. J. Paier, R. Asahi, R. Wahl, and G. Kresse, Phys. Rev. B 79, 115126 (2009).
16. S. Chen, X. G. Gong, A. Walsh, and S.-H. Wei, Appl. Phys. Lett. 96, (2010) 021902; S. Chen, J.-H.
Yang, X. G. Gong, A. Walsh, and S.-H. Wei, Phys. Rev. B. 81, (2010) 245204.
17. A. Nagoya, R. Asahi, R. Wahl, and G. Kresse, Phys. Rev. B. 81, (2010) 113202
18. Hiroshi Nozaki, Tatsuo Fukano, Shingo Ohta, Yoshiki Seno, Hironori Katagirib, Kazuo Jimbo.
524, (2012) 22–25
19. Xiancong He, Honglie Shen. j. Physica B: Condensed Matter. 406, (2011) 4604–4607
20. Clas Persson. J. Appl. Phys. 107, (2010) 053710
21. Shiyou Chen, X. G. Gong, Aron Walsh, Su-Huai Wei. APPLIED PHYSICS LETTERS. 94, (2009)
041903
22. Bonazzi P., Bindi L., Bernardini G.P., Menchetti S. Canadian Mineralogist. 41, (2003), p. 639-
647.
23. Olekseyuk I.D., Gulay L.D., Dydchak I.V., Piskach L.V., Parasyuk O.V., Marchuk O.V. J. Alloys.
Compd. 340 (2002), p. 141 - 145.
24. A.O. Fedorchuk, O.V. Parasyuk, I.V. Kityk. Maer.ChemPhys. V.139, (2013), 92
25. Emsley J. The Elements (Oxford University Press, Oxford, 1997).
26. P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka and J. Luitz, WIEN2k, Vienna University of
Technology, Austria (2001).
27. W. Kohn and L. J. Sham, Phys. Rev. A 140, 1133 (1965).
28. J. P. Perdew, S. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865.
29. E. Engel, S. H. Vosko, Phys. Rev. B. 47 (1993) 13164.
30. Fabien Tran and Peter Blaha Phys. Rev. Lett. 102, (2009) 226401
31. Shiwu Gao, Computer Physics Communications, 153, (2003) 190
32. Karlheinz Schwarz, Journal of Solid State Chemistry. 176, (2003) 319
33. Dovgii, Ukr.Phys.Journal, 1984
34. A. Delin, P. Ravindran, O. Eriksson, J. M. Wills, Int. J.Quant. Chem. 69 (1998) 349-
35. 358.
36. Ya.O.Dovgii, .I.V. Kityk, M.I. Kolinko, A.S. Krochuk, A.V. Franiv & M.K. Zamorskii.
Phys.Stat.Sol. V.167B. (1991).P.637-646.
37. K.Nouneh, A.H.Reshak, S.Auluck, I.V.Kityk, R.Viennois, S.Benet, S.Charar. Journal of Alloys
and Compounds, V.437, (2007), pp.39-46; Ali Hussain Reshak, Dalibor Stys, S. Auluck and I. V.
Kityk. . Journal Physical Chemistry B. V. 113, (2009), pp 12648–12654.
38. H. Tributsch, A. Naturforsch. 32A (1977) 972.
39. D.R. Penn, Phys. Rev. B.128 (1962) 2093-2097.
40. M. Fox, Optical Properties of Solids, Oxford University Press, 2001.
41. L. Marton, Rev. Mod. Phys. 28 (1956) 172-184.
42. A. H. Reshak, H. Kamarudin, I. V. Kityk, S.Auluck. journal of material science, 48 (2013) 5157-
5162
Int. J. Electrochem. Sci., Vol. 9, 2014
974
43. Sikander Azam, A. H. Reshak. Int. J. Electrochem. Sci., 8 (2013) 10359 – 10375.
44. A.H. Reshak, S.A. Khan. Computational Materials Science 78 (2013) 91–97.
45. Saleem Ayaz Khan, A. H. Reshak. Int. J. Electrochem. Sci., 8 (2013) 9459 – 9473.
46. Ali H. Reshak, S. Auluck, I.V. Kityk. Current Opinion in Solid State and Materials Science 12
(2008) 14–18.
© 2014 by ESG (www.electrochemsci.org)
Recommended